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Campo Math.E

Rappresenta la base logaritmica naturale, specificata dalla costante, e.

Spazio dei nomi: System
Assembly: mscorlib (in mscorlib.dll)

public const double E
public static final double E
public const var E : double

Il valore di questo campo è 2.7182818284590452354.

Nell'esempio riportato di seguito viene confrontato E con il valore calcolato da una serie di potenze.

// Example for the Math.E field.
using System;

class EField 
{
    public static void Main() 
    {
        Console.WriteLine( 
            "This example of Math.E == {0:E16}\n" +
            "generates the following output.\n", 
            Math.E );
        Console.WriteLine( 
            "Define the power series PS(n) = Sum(k->0,n)[1/k!]" );
        Console.WriteLine( " (limit n->infinity)PS(n) == e" );
        Console.WriteLine( 
            "Display PS(n) and Math.E - PS(n), " + 
            "and stop when delta < 1.0E-15\n" );

        CalcPowerSeries();
    }

    // Approximate E with a power series.
    static void CalcPowerSeries()
    {
        double factorial = 1.0;
        double PS = 0.0;

        // Stop iterating when the series converges,
        // and prevent a runaway process.
        for( int n = 0; n < 999 && Math.Abs( Math.E - PS ) > 1.0E-15; n++ )
        {
            // Calculate a running factorial.
            if( n > 0 )
                factorial *= (double)n;

            // Calculate and display the power series.
            PS += 1.0 / factorial;
            Console.WriteLine( 
                "PS({0:D2}) == {1:E16},  Math.E - PS({0:D2}) == {2:E16}",
                n, PS, Math.E - PS );
        }
    }
}

/*
This example of Math.E == 2.7182818284590451E+000
generates the following output.

Define the power series PS(n) = Sum(k->0,n)[1/k!]
 (limit n->infinity)PS(n) == e
Display PS(n) and Math.E - PS(n), and stop when delta < 1.0E-15

PS(00) == 1.0000000000000000E+000,  Math.E - PS(00) == 1.7182818284590451E+000
PS(01) == 2.0000000000000000E+000,  Math.E - PS(01) == 7.1828182845904509E-001
PS(02) == 2.5000000000000000E+000,  Math.E - PS(02) == 2.1828182845904509E-001
PS(03) == 2.6666666666666665E+000,  Math.E - PS(03) == 5.1615161792378572E-002
PS(04) == 2.7083333333333330E+000,  Math.E - PS(04) == 9.9484951257120535E-003
PS(05) == 2.7166666666666663E+000,  Math.E - PS(05) == 1.6151617923787498E-003
PS(06) == 2.7180555555555554E+000,  Math.E - PS(06) == 2.2627290348964380E-004
PS(07) == 2.7182539682539684E+000,  Math.E - PS(07) == 2.7860205076724043E-005
PS(08) == 2.7182787698412700E+000,  Math.E - PS(08) == 3.0586177750535626E-006
PS(09) == 2.7182815255731922E+000,  Math.E - PS(09) == 3.0288585284310443E-007
PS(10) == 2.7182818011463845E+000,  Math.E - PS(10) == 2.7312660577649694E-008
PS(11) == 2.7182818261984929E+000,  Math.E - PS(11) == 2.2605521898810821E-009
PS(12) == 2.7182818282861687E+000,  Math.E - PS(12) == 1.7287637987806193E-010
PS(13) == 2.7182818284467594E+000,  Math.E - PS(13) == 1.2285727990501982E-011
PS(14) == 2.7182818284582302E+000,  Math.E - PS(14) == 8.1490370007486490E-013
PS(15) == 2.7182818284589949E+000,  Math.E - PS(15) == 5.0182080713057076E-014
PS(16) == 2.7182818284590429E+000,  Math.E - PS(16) == 2.2204460492503131E-015
PS(17) == 2.7182818284590455E+000,  Math.E - PS(17) == -4.4408920985006262E-016
*/

// Example for the Math.E field.
import System.*;

class EField
{
    public static void main(String[] args)
    {
        Console.WriteLine("This example of Math.E == {0}\n" 
            + "generates the following output.\n",
            ((System.Double)Math.E).ToString("E16"));
        Console.WriteLine("Define the power series PS(n) = Sum(k->0,n)[1/k!]");
        Console.WriteLine(" (limit n->infinity)PS(n) == e");
        Console.WriteLine(("Display PS(n) and Math.E - PS(n), " 
            + "and stop when delta < 1.0E-15\n"));
        CalcPowerSeries();
    } //main
 
    // Approximate E with a power series.
    static void CalcPowerSeries()
    {
        double factorial = 1.0;
        double pS = 0.0;
        // Stop iterating when the series converges,
        // and prevent a runaway process.
        for (int n=0; n < 999 && System.Math.Abs((Math.E - pS)) > 1E-15; n++) {
            // Calculate a running factorial.
            if (n > 0) {
                factorial *= (double)(n);
            }

            // Calculate and display the power series.
            pS += 1.0 /factorial;
            Console.WriteLine("PS({0}) == {1},  Math.E - PS({0}) == {2}",
                ((System.Int32) n).ToString("D2"),
                ((System.Double )pS).ToString("E16"),
                ((System.Double )(Math.E - pS)).ToString("E16"));
        } 
    } //CalcPowerSeries
} //EField

/*
This example of Math.E == 2.7182818284590451E+000
generates the following output.

Define the power series PS(n) = Sum(k->0,n)[1/k!]
 (limit n->infinity)PS(n) == e
Display PS(n) and Math.E - PS(n), and stop when delta < 1.0E-15

PS(00) == 1.0000000000000000E+000,  Math.E - PS(00) == 1.7182818284590451E+000
PS(01) == 2.0000000000000000E+000,  Math.E - PS(01) == 7.1828182845904509E-001
PS(02) == 2.5000000000000000E+000,  Math.E - PS(02) == 2.1828182845904509E-001
PS(03) == 2.6666666666666665E+000,  Math.E - PS(03) == 5.1615161792378572E-002
PS(04) == 2.7083333333333330E+000,  Math.E - PS(04) == 9.9484951257120535E-003
PS(05) == 2.7166666666666663E+000,  Math.E - PS(05) == 1.6151617923787498E-003
PS(06) == 2.7180555555555554E+000,  Math.E - PS(06) == 2.2627290348964380E-004
PS(07) == 2.7182539682539684E+000,  Math.E - PS(07) == 2.7860205076724043E-005
PS(08) == 2.7182787698412700E+000,  Math.E - PS(08) == 3.0586177750535626E-006
PS(09) == 2.7182815255731922E+000,  Math.E - PS(09) == 3.0288585284310443E-007
PS(10) == 2.7182818011463845E+000,  Math.E - PS(10) == 2.7312660577649694E-008
PS(11) == 2.7182818261984929E+000,  Math.E - PS(11) == 2.2605521898810821E-009
PS(12) == 2.7182818282861687E+000,  Math.E - PS(12) == 1.7287637987806193E-010
PS(13) == 2.7182818284467594E+000,  Math.E - PS(13) == 1.2285727990501982E-011
PS(14) == 2.7182818284582302E+000,  Math.E - PS(14) == 8.1490370007486490E-013
PS(15) == 2.7182818284589949E+000,  Math.E - PS(15) == 5.0182080713057076E-014
PS(16) == 2.7182818284590429E+000,  Math.E - PS(16) == 2.2204460492503131E-015
PS(17) == 2.7182818284590455E+000,  Math.E - PS(17) == -4.4408920985006262E-016
*/

Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile per Pocket PC, Windows Mobile per Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

.NET Framework non supporta tutte le versioni di ciascuna piattaforma. Per un elenco delle versioni supportate, vedere Requisiti di sistema.

.NET Framework

Supportato in: 2.0 1.1 1.0

.NET Compact Framework

Supportato in: 2.0 1.0

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